M E 433
Professor John M. Cimbala
Lecture 16
Today, we will:
•
Modify the Gaussian solution for a buoyant plume, and do some examples/applications
•
Compare a ground that absorbs the pollutant vs. one that does not absorb the pollutant
Gaussian plume model (steady with no buoyancy and no ground effect):
z
Side view
m j ,s
U
x
hs
2
2 
 
 1  y   z   
cj
exp −   +    , and we use empirical relations for the
We had:=
 
2p U s ys z
 2  s y   s z   
m j ,s
=
cx d + f , x in units of km and sy and sz in units of m.
dispersion coefficients: σ y = axb , σ
z
Modification for a buoyant plume:
m j ,s
U
x
U
hs
z
2 
   2 
z − H   
 1 y
exp −   + 
cj
Modified solution for a buoyant plume:=
 
s 
2p U s ys z
2
s

y

z
  
  
m j ,s
Ground effects (reflecting vs. absorbing ground):
Example: Gaussian plume dispersion coefficients
Given: A plant emits air pollution from a stack under the following conditions:
m j ,s
x
U
H
z
daytime with moderate solar radiation (summer day with a few clouds)
•
average wind speed = 4.0 m/s
To do:
(a) What stability class is this?
(b) What value of constant d should we use at x = 2.0 km to determine the dispersion
coefficient?
Solution:
(a) Use Table 20.1 to determine the stability class (see next page for table).
•
(b) Use Table 20.2 to determine constant d at x = 2.0 km (see table below).
Dispersion coefficients: Tables scanned from Cooper, C. D. and Alley, F. C. Air Pollution Control: A
Design Approach, Edition 4, Waveland Press, Inc., Long Grove, IL, 2011, pp. 662-663.
Summary of Gaussian plume model:
cx d + f , with x in units of km and sy and sz in units of m.
σ y = axb , σ=
z
With ground absorption,
2 
   2 
m j ,s
z − H   
 1 y
=
exp −   + 
cj
  , where H= hs + δ h = effective stack height.
s 
2p U s ys z
2
s


  
y
z
  
With ground reflection,
2 
2


   2 
   2 
m j ,s 

  
−
+
y
z
H
y
z
H
1
1
 


=
cj
exp −   + 
   + exp −   + 
   .


s
s
s
s
2p U s ys z 
2
2
  
  
z
z
  y  
  y  


Example: Gaussian plume
Given: A coal power plant emits NO2 under the following conditions:
z–H
m j ,s
x
U
H
z
hs
δh
stack height = 80 m
•
buoyant plume rise = 20 m above stack exit
•
average wind speed = 5.0 m/s
•
the stack emits the air pollutant at a rate of 110 g/s
•
overcast morning
•
the ground reflects (does not absorb) the air pollutant
To do: Estimate the maximum ground-level mass concentration of NO2 at x = 2.0 km.
Solution:
•
2 
2  

   2 
   2 


−
+
y
z
H
y
z
H
1
1



exp −   +
  + exp −   + 
 
=
cj



 
s
2p U s ys z 
2  s 

 2  s y   s z   
  y   z   

m j ,s